A novel design of unknown input observers using set-theoretic methods for robust fault detection

Abstract

This paper proposes a novel unknown input observer (UIO) design method, which incorporates the set theoretic notions into the design of UIOs. In this way, we can take advantage of both UIOs and set-theoretic methods in fault detection (FD). The main advantage of UIOs is that they can be insensitive to unknown inputs affecting a system. However, a critical limitation is the satisfaction of the UIO design conditions for a monitored system. The core idea of this paper is that, even though we cannot design a UIO insensitive to all unknown inputs, we can at least design a UIO insensitive to as many unknown inputs as possible. In this case, although the effect of all unknown inputs on FD cannot be completely removed, we can at least partially remove the effect of unknown inputs. Furthermore, for the remaining unknown inputs whose effect cannot be removed, the set-theoretic methods can be employed to specify them and obtain FD robustness against their effect. At the end of this paper, the effectiveness of the proposed method is illustrated by a numerical example.